Selective area doping for Mott neuromorphic electronics

The cointegration of artificial neuronal and synaptic devices with homotypic materials and structures can greatly simplify the fabrication of neuromorphic hardware. We demonstrate experimental realization of vanadium dioxide (VO2) artificial neurons and synapses on the same substrate through selective area carrier doping. By locally configuring pairs of catalytic and inert electrodes that enable nanoscale control over carrier density, volatility or nonvolatility can be appropriately assigned to each two-terminal Mott memory device per lithographic design, and both neuron- and synapse-like devices are successfully integrated on a single chip. Feedforward excitation and inhibition neural motifs are demonstrated at hardware level, followed by simulation of network-level handwritten digit and fashion product recognition tasks with experimental characteristics. Spatially selective electron doping opens up previously unidentified avenues for integration of emerging correlated semiconductors in electronic device technologies.


INTRODUCTION
Neuromorphic computing represents a computational paradigm that aims to emulate characteristics of information processing in the brain. Mott semiconductors offer a powerful platform to realize neuromorphic hardware via electrically driven conductance transitions (1)(2)(3). For instance, a single vanadium dioxide (VO 2 ) device connected to a capacitor can serve as an oscillatory artificial neuron in a more compact manner (4-7) compared to traditional silicon (Si) complementary metal-oxide semiconductor layouts. While individual artificial neurons and synaptic primitives have been demonstrated with correlated electron semiconductors demonstrating substantial potential (8)(9)(10)(11)(12)(13), interconnected networks made of neurons and synapses at hardware level and relevant fabrication processes for Mott circuits are in their infancy. While implementation of hardware-based neuromorphic test structures have been reported in literature (14)(15)(16), the interconnected neuronal and synaptic components usually adopted heterotypic material systems and device structures.
We hypothesize that the ability to perform multiple neural functions with the same material system can simplify the chip-scale fabrication process among other benefits. Especially when new materials that have never been introduced in a fab are being considered, if they can offer more than one compelling device application within the same technology domain, then the chances of their consideration naturally become greater. However, this requires innovation in the implementation of diverse neural functions into identical devices after fabrication. For this purpose, we borrow the concept of selective doping from integrated circuit industry and apply them to quantum materials. Selective area doping, which is effective not only for traditional semiconductors (e.g., Si and III-V compounds) but also for emerging materials [e.g., two-dimensional materials (17)(18)(19)], is used across the spectrum of semiconductor technologies to create solid-state devices, such as junctions, contacts, transistors, and inversion layers. Adapting this approach to Mott semiconductors represents a promising direction.
At the outset, we note that there are profound differences in doping physics between band semiconductors such as Si and Mott semiconductors such as VO 2 (20). In Si and related materials, aliovalent doping concentration in the order of parts per million is sufficient for repositioning the Fermi level or band edges for function, whereas in Mott materials, doping density in the order of 0.1 to 1 electron per unit cell (i.e.,~10 5 to 10 6 larger doping density) is needed to induce conductance changes (21,22). Hence, strategies for doping Mott semiconductors that can be scalable and viable for semiconductor technologies are a nontrivial problem.
The principal objective of this study is to experimentally demonstrate the cointegration of artificial neuronal and synaptic components with homotypic material systems and device structures on chip by spatially selective hydrogen donor doping of VO 2 . This is demonstrated by careful design of catalytic and inert electrode pairs and experimental measurements of electrical properties. Hydrogen as a dopant (23)(24)(25) performs two important and unique functions here: reduces the insulating ground-state resistance and controls the memory state retention (i.e., volatility versus nonvolatility) in two-terminal Mott devices. Hydrogen is selectively doped using catalytic metal electrodes (e.g., Pd), such that the hydrogenated devices can serve as synapses for learning and memory, while pristine undoped devices can function as neurons for signal transfer. Therefore, by spatially selective doping, we are able to realize the two most sought-after neuromorphic functions essential for neural networks with the same parent material. The gentle forming gas (5% H 2 ) anneal process causes no lattice damage, and both ground-state resistance and volatility of the memory are tunable. By suitable lithographic design of catalytic and inert electrodes, both volatile and nonvolatile devices with homotypic materials and structures can be integrated on a single chip (Fig. 1, A and  B). As proof of principle, neural circuit motifs are then fabricated and demonstrated at hardware level to emulate excitation/inhibition functions. With the experimental characteristics, network-level recognition tasks are further simulated on the Modified National Institute of Standards and Technology (MNIST) (26) and Fashion-MNIST (27) datasets with test accuracies comparable to other state-of-the-art unsupervised approaches (Fig. 1, C and D).

RESULTS
Spatially selective hydrogenation of VO 2 VO 2 can be hydrogen-doped via a variety of methods, such as hightemperature annealing (28), electrochemical insertion (10,29), and catalytic spillover (23,24). This work uses the catalytic spillover method to demonstrate selective doping, which occurs at backend compatible low process temperatures (fig. S1). Palladium (Pd) is a commonly used catalytic electrode in hydrogen spillover process (30), and it is also effective toward catalytic hydrogen doping of VO 2 (31,32). The inserted hydrogen dopants (i.e., protons) occupy interstitial sites among VO 2 lattices and bond with oxygen atoms along with electron transfer ( Fig. 2A and fig. S2). The electron doping effect can be observed in the vanadium L 2,3 and oxygen K-edges from the electron energy loss spectra in Fig. 2B and fig.  S3. The relative intensity ratio of t 2g peak over e g peak in hydrogenated VO 2 (H x VO 2 ) is much decreased compared with that in pristine VO 2 , indicating that more states at the lower t 2g level are filled by electrons. Meanwhile, the vanadium L 2,3 edge shows a red shift, which is consistent with the valence state change from V 4+ to V 3+ as a result of higher V 3d orbital occupancy (33). X-ray diffraction (XRD) spectra (Fig. 2C) also reflect the Pd catalyst-assisted hydrogen spillover process. A 50-nm-thick pristine VO 2 thin film has a monoclinic (020) M peak at 39.8°[equivalent to a rutile (200) R peak] at room temperature. After the hydrogenation with Pd electrodes, the diffraction peak of (200) R shifts to 36.2°, indicating the out-of-plane lattice expansion (23).
Compared with the Pd electrode, the TiAu electrode is less active in the hydrogen spillover process (34). The VO 2 film with the TiAu electrodes remains identical in its XRD spectrum after the hydrogenation, and the region near TiAu is still in its original gray color (indexed as VO 2 ) ( fig. S4). It indicates that negligible doping occurs at the TiAu-VO 2 -H 2 triple-phase boundary. Therefore, by selecting the combination of catalytic (Pd) and inert (TiAu) electrodes, proton distribution across the device channels in twoterminal VO 2 devices (Fig. 2D) can be controlled. To visualize the proton distribution, the surface current of devices with different electrode pairs were probed using a conductive atomic force microscope (C-AFM) after the hydrogenation ( fig. S5). For the VO 2 device with two inert TiAu electrodes (i.e., TiAu + TiAu device), the probed current in the channel shows low intensity, indicating an insulating nature of VO 2 and that no protonation occurred during the hydrogenation. In contrast, for the VO 2 device with Pd electrodes (i.e., Pd + Pd device), the probed current becomes higher, indicating proton distribution across the whole channel. The Pd + Pd device shows metallic H x VO 2 behavior, where both thermally and electrothermally driven insulator-metal transition phenomena are not observed (figs. S6 and S7). Here, we refer to electrothermally driven insulator-metal transition as E-IMT. For the device with an asymmetric electrode pair (i.e., TiAu + Pd device), the probed current decreases monotonically across the channel from Pd to TiAu electrodes, as shown in Fig. 2E. The proton distribution was further mapped using Raman spectroscopy. All the peaks observed in the channel are in good agreement with the reported monoclinic VO 2 results (35). On the other hand, the metallic rutile H x VO 2 has no Raman peaks in this range (100 to 800 cm −1 ) (36). Thus, by comparing the intensity of characteristic VO 2 peak (at 615 cm −1 ) measured at different locations within the channel, a decrease of proton density across the channel from Pd to TiAu was observed, indicating a transition from H x VO 2 to VO 2 ( Fig. 2F and fig. S8). By subtly controlling hydrogenation level and proton distribution, more intermediate states are accessible. Figure 2G shows temperature-dependent resistance of the device with asymmetric electrode pairs at different hydrogenation levels. The ground-state resistance continues to decrease with increase of hydrogenation time and eventually becomes comparable to the resistance after the phase transition. The hydrogenation also tunes the electrothermally driven transition behavior of H x VO 2 device ( Fig. 2H and fig. S9). Depending on the hydrogen doping, threshold voltage (V th ) for triggering the E-IMT decreases from 3.6 to~0.6 V. Further hydrogenation can induce a nonvolatile current-voltage relation (I-V ) hysteresis characteristic of the device. Such a nonvolatility is reversible, and the volatile E-IMT phenomenon is reproducible in dehydrogenated devices ( fig. S10).

Volatile and nonvolatile memory in (H x )VO 2 devices
With different combinations of Pd and TiAu electrodes, the VO 2 devices can show tunable volatility enabled by different proton distributions across the channels after the selective hydrogenation. The TiAu + TiAu devices retain the pristine VO 2 channels and exhibit threshold switching with symmetric I-V hysteresis loops in both positive and negative bias polarities, as shown in Fig. 3A and fig.  S11. V th , above which the E-IMT is triggered by Joule heating due to the flowing current, and holding voltage (V hold ), below which the relaxation happens, are ±3.2 and ±1.5 V on average, respectively. The devices retain a clear gap between V th and V hold for reliable operation (figs. S12 and S13). The devices show stable volatile characteristics with no resistance changes after multicycle electric pulse stimuli are applied (Fig. S14). These results indicate that the TiAu + TiAu device can be used to emulate artificial neurons, and the well-known leaky integrate and fire (LIF) neuron functions are demonstrated, as shown in Fig. 3B. The TiAu + TiAu device is connected to a load resistor (R L ) in series and a capacitor (C M ) in parallel. Current pulses are applied to the circuit and once the potential across the TiAu + TiAu device reaches V th through C M charging, the device can be switched from the off-state to the on-state with a sudden increase of current flow (Fig. 3C). The firing rate is tunable upon the capacitor and the input current pulses [including pulse width (t p ), amplitude (A p ), and duty ratio (D p )] (figs. S15 to S19). Apart from current pulses, voltage pulses are also effective to activate the LIF neuron circuit and to modulate the firing behavior ( fig. S20).
On the other hand, the TiAu + Pd devices show a nonvolatile characteristic after the hydrogenation. As shown in Fig. 3D, there is a combination of nonvolatile resistive switching and volatile threshold switching (with a V th of~2.4 V) in the positive bias polarity of I-V curves even after 1000 sweeps. Considering that the undoped TiAu + Pd devices exhibit threshold switching only, this unique phenomenon should be attributed to the partially hydrogendoped channels, which are a mixture of VO 2 and H x VO 2 . Because protons are able to drift in the channel under an external electric field, we can observe the changes of device resistance upon consecutive I-V sweeps and multicycle electric pulses, and the devices maintain their resistance states for >10 4 s after the removal of electrical stimuli (figs. S21 to S23). Such a nonvolatile feature widely exists in the doped TiAu + Pd devices with reasonable cycle-tocycle and device-to-device variations (fig. S24).
The insertion of protons into the H x VO 2 channels introduces intermediate resistance states to the hydrogenated TiAu + Pd devices, which can be used to design artificial synapses. As shown in fig. S25A, upon consecutive positive or negative electric pulse stimuli, device resistance and hence synaptic weight (w) can be repeatedly programmed. The change of device resistance is dependent on the applied voltage pulse amplitude and width. For example, when the pulse amplitude increases from 8 to 10 V/μm, the updated resistance after 50 consecutive pulses is doubled (Fig. 3E). When the pulse width increases from 1 to 10 μs, the resistance difference after 50 consecutive pulses reaches about nine times ( fig. S25B). Under different pulse conditions, the TiAu + Pd devices perform a relatively linear resistance potentiation with an extracted nonlinear factor of~0.8 ( fig. S26). This is beneficial for the enhancement of training accuracy in spiking neural networks (SNNs) using the hydrogenated TiAu + Pd devices as synapses (37).
The multiple metastable states in the devices and their impact on the resistance states are elucidated by density functional first-principles calculations. Figure 3F shows the relative stability analysis based on the total energy differences between pseudomonoclinic H x VO 2 (M1) and pseudorutile H x VO 2 (R) phases with different concentrations of H dopants. The simulation results reveal that the pseudomonoclinic phase (light sea green region) is more favorable when x is ≤0.25 atomic fraction of a H x VO 2 formula unit. Upon further doping, the pseudorutile phase becomes more stable (light magenta regime). By accessing the electronic properties in terms of the total and partial density of states (DOS) at different hydrogenation levels, we observe that the intermediately doped H x VO 2 (R) phase retains a metallic characteristic with increasing H doping (0.25 < x ≤ 0.5), while the increase of H content in the lightly doped H x VO 2 (M1) phase reduces its bandgap before transitioning into this metallic state ( fig. S27). The reduction of bandgap is attributed to the partial occupation of d || */π* orbitals upon the addition of hydrogen and is reflected in the shifting down of the occupancy of d || (d x2−y2 ) orbitals ( fig. S28). Across the lightly hydrogenated TiAu + Pd device channels, there should be a portion of the semiconducting H x VO 2 region with x value ranging between 0 and 0.25. Upon application of external electric field, the migration of protons results in the update of the x value in H x VO 2 locally. Because the change of bandgap affects the resistivity of the semiconducting regions, their redistribution can bring about tunable intermediate resistance states to the synaptic devices.

Design and fabrication of cointegrated neural circuit motifs with (H x )VO 2 devices
Through selective area doping, both volatile and nonvolatile (H x )VO 2 devices can be integrated on a single chip (see Materials and Methods and fig. S29). Their interconnections allow the demonstration of feedforward excitation/inhibition neural circuits, which are fundamental micronetwork motifs. The circuit hardware primarily consists of a presynaptic neuron (N1), a postsynaptic neuron (N2), a synapse, and peripheral circuits (Fig. 4, A and B). The two neurons are connected in series through a synapse to control spiking signal transmission from N1 to N2 by adjusting the weight. To avoid detrimental voltage fluctuations due to signal interferences, operational amplifiers (op-amps) are introduced between neural components. Specifically, a voltage follower [i.e., isolator 1 (Iso1)] is placed between the N1 and the synapse (38), and an inverting amplifier plus a Howland current pump (39,40) for voltage-to-current conversion (i.e., Iso2) are installed between the synapse and the N2 (41). The synaptic weight (w) here is defined as the absolute value of the inverting amplifier's gain (i.e., the ratio of the resistance across the op-amp over the effective synapse resistance) ( fig. S30). By tuning the input current pulses, we can directly modulate the spikes emanating from N1. Because of the existence of Iso1, the downstream synapse has little impact on N1, showcasing similar spiking characteristics under different synaptic weights ( fig. S31). However, before transferring into N2, the ejected spike train needs to be processed by the synapse, so the firing of N2 is closely related to the synaptic weight. As shown in Fig. 4 (D and E), with the decrease (increase) of synaptic weight, the firing probability of N2 decreases (increases), indicating that the N2 behaves like an inhibitory (excitatory) neuron. The feedforward excitation/inhibition neural circuits are further simulated using Simulation Program with Integrated Circuit Emphasis (SPICE). The neuronal behavior can be well reproduced using an equivalent circuit consisting of a threshold switch and a capacitor ( fig. S32). The simulated spiking behaviors of N1 and N2 under different synaptic weights and input current pulses are in good agreement with the results measured in hardware ( Fig. 4C and fig. S33). The consistency of simulation and measurement results augment the credibility of recognition tasks that are executed in the (H x )VO 2 neural networks. In this work, Iso1 and Iso2 were inserted in the connection between one synapse and one neuron, but it is not necessary to reserve an exclusive isolator for each synapse-neuron pair when the connection scales up (i.e., between multiple synapses and one neuron). These isolators can be shared by serving as a part of neuron peripheral circuitry wherein multiplexers and demultiplexers are included between adjacent neural layers and multiple synapses are connected in parallel.

(H x )VO 2 -based SNNs
To showcase the excitatory and inhibitory neural circuits using both volatile and nonvolatile (H x )VO 2 devices in the context of networklevel recognition tasks, an SNN was designed using the experimental data from the devices. SNNs use "spikes" and learning occurs by modulating the synaptic weights based on the relative timing of the spikes, known as spike timing-dependent plasticity (STDP) (42). The local, sparse, and unsupervised nature of STDP lends itself to low-power on-chip embedded intelligence applications. The network architecture for the SNN is shown in Fig. 1C. The network is made of volatile VO 2 neurons connected by nonvolatile H x VO 2 synapses. In hardware implementations, such a system can be mapped to a cross-array of synapse devices, terminating at neuronal devices. The stochastic switching of the neuron was sigmoidal in nature (Fig. 4F). The linear potentiation of the H x VO 2 was used in simulating the synaptic conductance change. We trained the network on the MNIST (26) and Fashion-MNIST (27) datasets, each consisting of 10 classes of 28-by-28 pixel grayscale images of handwritten digits and fashion products, respectively. Both datasets used in the simulations were composed of 60,000 training samples and 10,000 test samples. The inputs to the network were Poisson spike trains, generated from the image pixel values. In addition, for the Fashion-MNIST, the dataset was filtered using the Sobel filter for edge detection before converting to spikes. The simulated networks consisted of an input layer of size 784 (equivalent to the dimensionality of the input data), an excitatory layer, and an inhibitory layer of 1600 each for MNIST and 400 each for Fashion-MNIST. All the neurons in the excitatory layer are connected to all the neurons in the input layer with excitatory connections. The neurons in the inhibitory layer are connected to one For the sake of clarity, H x VO 2 (M1) and H x VO 2 (R) are in pseudomonoclinic and pseudorutile phases, respectively, since the presence of protons alters the ideal lattice parameters and bond distances of both the pristine monoclinic and rutile phases. The light sea green region describes the zone where H x VO 2 (M1) is more favorable, whereas the light magenta regime indicates that H x VO 2 (R) is more stable. Insets (i), (ii), (iii), and (iv) are the total density of states (DOS) of the lowenergy phases of 0.0, 0.03, 0.25, and 0.50 atomic fraction of H levels in H x VO 2 , respectively. With increasing H dopant level, the semiconducting monoclinic H x VO 2 phase (i) narrows its bandgap from~0.61 to 0.5 eV as seen in (ii). Upon further doping, it changes to metallic (iii) in its pseudomonoclinic phases and its pseudorutile phases (iv).
corresponding excitatory neuron with excitatory synapses and with inhibitory synapses to all the rest. The inhibitory connections achieve winner-take-all functionality in the SNN. The employment of the inhibitory connections greatly increases the generalization capability of the network, as shown in fig. S34. Note that only the excitatory connections from the input to the excitatory layer are tunable, while the other synaptic conductance remains static. Details of the network simulation can be found in Materials and Methods. After training, three independent test runs on the two datasets were performed. The simulated networks achieved an average test accuracy of 73.29% (SD: 0.09%) for Fashion-MNIST (Fig. 4G) and 92.26% (SD: 0.05%) for MNIST (Fig. 4H). These accuracies are in line with state-of-the-art unsupervised approaches for both datasets (43,44), demonstrating the efficacy of (H x )VO 2 devices for scalable neuromorphic systems.

DISCUSSION
Selective area electron doping is demonstrated for archetypal Mott oxide electronic devices using insulator-metal transitions. This process enables monolithic integration of homotypic volatile threshold firing neurons and nonvolatile synapses for memory, providing a platform to implement Mott neuromorphic hardware for brain-inspired computing electronics and neural systems emulation studies. In the long term, the approach presented here can be of use to various emerging semiconductors that require heavy concentrations of dopants in device technologies.

VO 2 thin-film deposition
Before deposition, 10-by-10 mm 2 c-plane sapphire substrates were cleaned through an ultrasonic bath of toluene, acetone, and isopropyl alcohol in sequence. The 50-nm-thick VO 2 thin films were deposited using an ultrahigh vacuum magnetron sputtering system from AJA International Inc. During deposition, a V 2 O 5 ceramic target was used in the deposition powered with a radio frequency source at 100 W. The substrate temperature was 650°C. The chamber pressure was set at 5 mTorr of the Ar/O 2 mixture with a ratio of 99.9/0.1. The deposition rate was 0.6 nm/min. Before material characterizations, the H x VO 2 samples were annealed at 200°C in a homebuilt furnace filled with a forming gas (5% H 2 balanced by 95% Ar) for 30 min.
(H x )VO 2 device fabrication Both volatile (TiAu + TiAu) and nonvolatile (TiAu + Pd) VO 2 devices were fabricated on a single sapphire substrate. After substrate cleaning and 50-nm-thick VO 2 thin-film deposition, the thin film was patterned using argon ion milling, during which SPR-220-3.5 photoresist served as a mask layer. Next, Ti (10 nm)/ Au (100 nm) contact pads were formed through photolithography with LOR-3A and S1813 photoresists, electron beam evaporation (Ti deposition came first), and liftoff in Remover PG (Kayaku Advanced Materials,.Inc) at 80°C. To define the submicrometer channels, electron beam lithography was used in the next steps, where 495 poly(methyl methacrylate) (PMMA) A4 and 950 PMMA A4 were used as photoresists. Ti (10 nm)/Au (50 nm) stripes in the TiAu + TiAu and the TiAu + Pd devices were patterned by electron beam evaporation and liftoff in acetone at room temperature. The 50-nm-thick Pd electrode strips in the TiAu + Pd devices were patterned by repeating the processes for the TiAu electrode strips. The fabricated devices were annealed at 100°C in the forming gas with a flow rate of 50 standard cubic centimeter per minute to selectively hydrogenate the TiAu + Pd VO 2 device. For the feedforward excitation/inhibition neural circuits, the volatile and nonvolatile devices on the same chip were interconnected by further wire bonding to a chip carrier.

Electrical measurements
The electrical performance of (H x )VO 2 device was characterized at room temperature by a Keithley 4200A-SCS parameter analyzer with ultrafast pulse measure units (4225-PMU) and remote preamplifier/switch modules (4225-RPM), which can apply submicrosecond electric pulses. For all electrical measurements, the TiAu electrode was connected to the ground. For (H x )VO 2 neural circuits, in situ I-V measurement setups were designed and customized. The pulse trains applied across the circuits were generated by an arbitrary function generator (Tektronix AFG31000 Series), while the voltage signals were monitored using an oscilloscope (Tektronix DSOX4154A). A high-speed voltage-to-current converter was connected to the arbitrary function generator for applying microsecond current pulses to the (H x )VO 2 neural circuits. For the neuronal behavior, the TiAu + TiAu VO 2 device was connected in series with a 200-ohm load resistor (R L ) and a 4.4-nF capacitor (C M ) in parallel. The voltage drops across the VO 2 device (V VO2 ), and the R L (V out ) were acquired from the oscilloscope. The current passing through the TiAu + TiAu VO 2 device was calculated with the equation I = V out /R L . For testing the individual neuron behavior in connected neuron-synapse-neuron circuits, customized isolators were used between the three components to avoid signal interferences among these devices, which might adversely affect signal propagation throughout the circuit.

Simulation methodology for neural circuits
Both single neuronal component and neural circuit behaviors were simulated with LTspice. The TiAu + TiAu VO 2 device was modeled as a threshold switch highlighted by a red dash box, as shown in fig.  S32A. The off-state resistance (R H ) of the threshold switch was constant, while the on-state resistance (R L ) was controlled by the voltage across the threshold switch (V in − V out ). Meanwhile, a minimum R L (i.e., R min ) was imposed through the transition voltage (V sim ). If V in − V out > V sim , then the on-state resistance would be directly assigned with R min . If V in − V out < V sim , then the relationship between R L and V in − V out follows an empirical formula acquired through fitting the I-V characteristic in fig.  S32B; i.e., R L = 1000/[α + β × (V in − V out ) + γ × (V in − V out ) 2 ]. The parameters for single neuronal component simulations are listed in table S1 and fig. S32D. In the neural circuit simulation, a programmable resistor serving as the synapse was connected between Iso1 and Iso2. Because pre-and postsynaptic neurons showed stochasticity, their parameters used in the simulation (table S2) were individually adjusted to fit their own behaviors better.

Simulation methodology for network-level recognition tasks
SNNs use bioplausible local learning mechanisms motivated by the propagation of electric impulses in the biological brain, often referred to as STDP (45,46). In STDP, the synaptic weights are modified in an exponential manner based on the relative timing difference between pre-and postsynaptic neuronal activities. The SNN implementation was done using a modified version of Bind-sNET (47), an open-source PyTorch-based framework. The network architecture was adopted from (43) for both the MNIST and Fashion-MNIST datasets. The stochastic neuron model with the VO 2 neuron dynamics was used. The linear potentiation of the H x VO 2 synapse with four-bit discretization was taken. The weight dynamics is computed using synaptic traces (48), and the weight update rule is characterized by Δw ¼ η post � χ pre on postsynaptic spike À η pre � χ post on presynaptic spike � ð1Þ Here, χ pre and χ post are the pre-and postsynaptic traces, respectively, and are set to 1 whenever the pre-or postsynaptic neurons fire and decay exponentially to 0 with decay time constant τ trace . η post /η pre represent the pre-and postsynaptic learning rates. To mimic quantized weight updates typically observed in such device technologies (49), the weights in the network-level simulations were quantized using Here, w and w q are the nonquantized and quantized weights, respectively, and N is the quantization precision. Lateral inhibition is implemented using the inhibition layer and its inhibitory connections. To stop a single neuron from dominating the learning process, homeostasis was implemented by adaptively scaling the input to the stochastic neuron. The network parameters are given in table S3.

Supplementary Materials
This PDF file includes: Supplementary Text Figs. S1 to S34 Tables S1 to S3 References